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## anonymous one year ago Please help. I need help with a couple of questions. I will give medal and fan.

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1. anonymous

A toy rocket was launched from the ground. The function f(x) = -16x^2 + 192x shows the height of the rocket f(x), in feet, from the ground at time x seconds. What is the axis of symmetry of the graph of f(x), and what does it represent? x = 12; it takes 12 seconds to reach the maximum height and 12 seconds to fall back to the ground x = 12; it takes 12 seconds to reach the maximum height and 24 seconds to fall back to the ground x = 6; it takes 6 seconds to reach the maximum height and 6 seconds to fall back to the ground x = 6; it takes 6 seconds to reach the maximum height and 3 seconds to fall back to the ground

2. anonymous

I think its either C or D

3. anonymous

i think it is not a 100% sure though

4. anonymous

can you help me with a couple more?

5. anonymous

yeah i will try

6. anonymous

Functions f(x) and g(x) are shown below: f(x) = x2 g(x) = x2 + 10x + 25 In which direction and by how many units should f(x) be shifted to obtain g(x)? Right by 5 units Left by 5 units Right by 10 units Left by 10 units

7. Vocaloid

hint: (x^2 + 10x + 25) = (x+5)^2

8. anonymous

so would it be D?

9. Vocaloid

nope, please look carefully at what I wrote (x+k)^2 moves the graph x^2 to the left k units

10. anonymous

OK, B?

11. Vocaloid

yes, B is the answer, but do you understand how to get (x+5)^2?

12. anonymous

can you explain it a little, I sort of forgot.

13. Vocaloid

have you seen this formula? (a+b)^2 = a^2 + 2ab + b^2?

14. anonymous

yes

15. Vocaloid

great! in the equation x^2 + 10x + 25, do you see how x = a and b = 5? when you plug in x for a and b for 5, do you see how x^2 + 10x + 25 = (x+5)^2? this is called "factoring", basically you want to find a and b so you can simplify x^2 + 10x + 25 into (x+5)^2

16. anonymous

oh, I remember thanks!

17. anonymous

do you mind helping me with a couple more?

18. Vocaloid

sure, I guess

19. anonymous

The steps to derive the quadratic formula are shown below: Which of the following statements best describes the first incorrect step? In Step 4, square of quantity of b over 2 times a instead of b over 2 times a was added on both sides. In Step 5, x plus b over 2 times a, all squared was written instead of x plus b over 4a, all square. In Step 6, c over a was written instead of -c over a inside the root. In Step 7, square of quantity of b over 2 times a was written instead of b over 2 times a inside the root.

20. Vocaloid
21. Vocaloid

NOTE: I got this from a website, I didn't write this out myself, but these are the steps to derive the quadratic equation

22. anonymous

David kicks a soccer ball off the ground and in the air, with an initial velocity of 35 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches?

23. anonymous

for this one I know you plug in the 35 for v but what do you plug in for s?

24. Vocaloid

v = initial velocity = 35, s = initial height = 0

25. Vocaloid

an object on the ground has a height of 0

26. Vocaloid

initial height = 0, because the ball is on the ground

27. anonymous

ok I can do this one by myself

28. Vocaloid

k cool

29. anonymous

can you help me with 3 more?

30. Vocaloid

ok

31. anonymous

Water coming out from a fountain is modeled by the function f(x) = -x2 + 7x + 5 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 4 to x = 6 represent? The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds. The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds. The water travels an average distance of 5 feet from 4 seconds to 6 seconds. The water travels an average distance of 3 feet from 4 seconds to 6 seconds.

32. anonymous

If 5p = -100 + 3Q2, which of the following could Q possibly be? Q = square root of 5p-100/ 3 Q = square root of 5p+100/3 Q = square root of -5p+100/ 3 Q = square root of -5p-100/ 3

33. Vocaloid

this one is a bit tough to explain but I'll try average rate of change = speed = distance/time the average rate of change between x = 6 seconds and x = 4 seconds = distance travelled between 4 to 6 seconds/(6-4 seconds) = [f(6)-f(4)]/(6-4)

34. Vocaloid

and for the second one: 5p = -100 + 3Q^2 all you're doing is solving for Q in terms of p add 100 to each side divide each side by 3 take the square root of each side to find Q

35. anonymous

35p=q^2 I got 5.9160797830996160425673282915616 when I did the square root of 35

36. Vocaloid

??? I think you're confused, can I try outlining it step by step?

37. anonymous

sorry I got confused I understand now.

38. Vocaloid

|dw:1432846015012:dw|

39. anonymous

the answer I got is B

40. Vocaloid

yup! good job

41. anonymous

|dw:1432846126778:dw|

42. anonymous

I have one more. Do you think you can help me?

43. anonymous

What is the domain of the following parabola? x ≥ 2 x ≤ -1 y ≤ 3 All real numbers

44. Vocaloid

are there any x values that don't have y values?

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